A new approach to observational cosmology using the scattering transform

TL;DR

This paper introduces the scattering transform as a robust, interpretable, and training-free statistical tool for extracting non-Gaussian information from cosmological fields, demonstrating its effectiveness in weak lensing parameter inference.

Contribution

It presents the scattering transform as a novel, stable, and interpretable method for cosmological parameter estimation, outperforming classic estimators and matching CNN performance without training.

Findings

Outperforms classic estimators on noisy simulated data

Matches state-of-the-art CNN performance

Provides stable and interpretable coefficients

Abstract

Parameter estimation with non-Gaussian stochastic fields is a common challenge in astrophysics and cosmology. In this paper, we advocate performing this task using the scattering transform, a statistical tool sharing ideas with convolutional neural networks (CNNs) but requiring no training nor tuning. It generates a compact set of coefficients, which can be used as robust summary statistics for non-Gaussian information. It is especially suited for fields presenting localized structures and hierarchical clustering, such as the cosmological density field. To demonstrate its power, we apply this estimator to a cosmological parameter inference problem in the context of weak lensing. On simulated convergence maps with realistic noise, the scattering transform outperforms classic estimators and is on a par with state-of-the-art CNN. It retains the advantages of traditional statistical descriptors, has provable stability properties, allows to check for systematics, and importantly, the scattering coefficients are interpretable. It is a powerful and attractive estimator for observational cosmology and the study of physical fields in general.